class Minuit: ''' A class for communicating with ROOT's function minimizer tool Minuit. ''' def __init__(self, number_of_parameters, function_to_minimize, parameter_names, start_parameters, parameter_errors, quiet=True, verbose=False): ''' Create a Minuit minimizer for a function `function_to_minimize`. Necessary arguments are the number of parameters and the function to be minimized `function_to_minimize`. The function `function_to_minimize`'s arguments must be numerical values. The same goes for its output. Another requirement is for every parameter of `function_to_minimize` to have a default value. These are then used to initialize Minuit. **number_of_parameters** : int The number of parameters of the function to minimize. **function_to_minimize** : function The function which `Minuit` should minimize. This must be a Python function with <``number_of_parameters``> arguments. **parameter_names** : tuple/list of strings The parameter names. These are used to keep track of the parameters in `Minuit`'s output. **start_parameters** : tuple/list of floats The start values of the parameters. It is important to have a good, if rough, estimate of the parameters at the minimum before starting the minimization. Wrong initial parameters can yield a local minimum instead of a global one. **parameter_errors** : tuple/list of floats An initial guess of the parameter errors. These errors are used to define the initial step size. *quiet* : boolean (optional, default: ``True``) If ``True``, suppresses all output from ``TMinuit``. *verbose* : boolean (optional, default: ``False``) If ``True``, sets ``TMinuit``'s print level to a high value, so that all output is logged. ''' #: the name of this minimizer type self.name = "ROOT::TMinuit" #: the actual `FCN` called in ``FCN_wrapper`` self.function_to_minimize = function_to_minimize #: number of parameters to minimize for self.number_of_parameters = number_of_parameters if not quiet: self.out_file = open(log_file("minuit.log"), 'a') else: self.out_file = null_file() # create a TMinuit instance for that number of parameters self.__gMinuit = TMinuit(self.number_of_parameters) # instruct Minuit to use this class's FCN_wrapper method as a FCN self.__gMinuit.SetFCN(self.FCN_wrapper) # set print level according to flag if quiet: self.set_print_level(-1000) # suppress output elif verbose: self.set_print_level(10) # detailed output else: self.set_print_level(0) # frugal output # initialize minimizer self.set_err() self.set_strategy() self.set_parameter_values(start_parameters) self.set_parameter_errors(parameter_errors) self.set_parameter_names(parameter_names) #: maximum number of iterations until ``TMinuit`` gives up self.max_iterations = M_MAX_ITERATIONS #: ``TMinuit`` tolerance self.tolerance = M_TOLERANCE def update_parameter_data(self, show_warnings=False): """ (Re-)Sets the parameter names, values and step size on the C++ side of Minuit. """ error_code = Long(0) try: # Set up the starting fit parameters in TMinuit for i in range(0, self.number_of_parameters): self.__gMinuit.mnparm(i, self.parameter_names[i], self.current_parameters[i], 0.1 * self.parameter_errors[i], 0, 0, error_code) # use 10% of the par. 1-sigma errors as the initial step size except AttributeError as e: if show_warnings: logger.warning("Cannot update Minuit data on the C++ side. " "AttributeError: %s" % (e, )) return error_code # Set methods ############## def set_print_level(self, print_level=P_DETAIL_LEVEL): '''Sets the print level for Minuit. *print_level* : int (optional, default: 1 (frugal output)) Tells ``TMinuit`` how much output to generate. The higher this value, the more output it generates. ''' self.__gMinuit.SetPrintLevel(print_level) # set Minuit print level self.print_level = print_level def set_strategy(self, strategy_id=1): '''Sets the strategy Minuit. *strategy_id* : int (optional, default: 1 (optimized)) Tells ``TMinuit`` to use a certain strategy. Refer to ``TMinuit``'s documentation for available strategies. ''' error_code = Long(0) # execute SET STRATEGY command self.__gMinuit.mnexcm("SET STRATEGY", arr('d', [strategy_id]), 1, error_code) def set_err(self, up_value=1.0): '''Sets the ``UP`` value for Minuit. *up_value* : float (optional, default: 1.0) This is the value by which `FCN` is expected to change. ''' # Tell TMinuit to use an up-value of 1.0 error_code = Long(0) # execute SET ERR command self.__gMinuit.mnexcm("SET ERR", arr('d', [up_value]), 1, error_code) def set_parameter_values(self, parameter_values): ''' Sets the fit parameters. If parameter_values=`None`, tries to infer defaults from the function_to_minimize. ''' if len(parameter_values) == self.number_of_parameters: self.current_parameters = parameter_values else: raise Exception("Cannot get default parameter values from the \ FCN. Not all parameters have default values given.") self.update_parameter_data() def set_parameter_names(self, parameter_names): '''Sets the fit parameters. If parameter_values=`None`, tries to infer defaults from the function_to_minimize.''' if len(parameter_names) == self.number_of_parameters: self.parameter_names = parameter_names else: raise Exception("Cannot set param names. Tuple length mismatch.") self.update_parameter_data() def set_parameter_errors(self, parameter_errors=None): '''Sets the fit parameter errors. If parameter_values=`None`, sets the error to 10% of the parameter value.''' if parameter_errors is None: # set to 0.1% of the parameter value if not self.current_parameters is None: self.parameter_errors = [max(0.1, 0.1 * par) for par in self.current_parameters] else: raise Exception("Cannot set parameter errors. No errors \ provided and no parameters initialized.") elif len(parameter_errors) != len(self.current_parameters): raise Exception("Cannot set parameter errors. \ Tuple length mismatch.") else: self.parameter_errors = parameter_errors self.update_parameter_data() # Get methods ############## def get_error_matrix(self): '''Retrieves the parameter error matrix from TMinuit. return : `numpy.matrix` ''' # set up an array of type `double' to pass to TMinuit tmp_array = arr('d', [0.0]*(self.number_of_parameters**2)) # get parameter covariance matrix from TMinuit self.__gMinuit.mnemat(tmp_array, self.number_of_parameters) # reshape into 2D array return np.asmatrix( np.reshape( tmp_array, (self.number_of_parameters, self.number_of_parameters) ) ) def get_parameter_values(self): '''Retrieves the parameter values from TMinuit. return : tuple Current `Minuit` parameter values ''' result = [] # retrieve fit parameters p, pe = Double(0), Double(0) for i in range(0, self.number_of_parameters): self.__gMinuit.GetParameter(i, p, pe) # retrieve fitresult result.append(float(p)) return tuple(result) def get_parameter_errors(self): '''Retrieves the parameter errors from TMinuit. return : tuple Current `Minuit` parameter errors ''' result = [] # retrieve fit parameters p, pe = Double(0), Double(0) for i in range(0, self.number_of_parameters): self.__gMinuit.GetParameter(i, p, pe) # retrieve fitresult result.append(float(pe)) return tuple(result) def get_parameter_info(self): '''Retrieves parameter information from TMinuit. return : list of tuples ``(parameter_name, parameter_val, parameter_error)`` ''' result = [] # retrieve fit parameters p, pe = Double(0), Double(0) for i in range(0, self.number_of_parameters): self.__gMinuit.GetParameter(i, p, pe) # retrieve fitresult result.append((self.get_parameter_name(i), float(p), float(pe))) return result def get_parameter_name(self, parameter_nr): '''Gets the name of parameter number ``parameter_nr`` **parameter_nr** : int Number of the parameter whose name to get. ''' return self.parameter_names[parameter_nr] def get_fit_info(self, info): '''Retrieves other info from `Minuit`. **info** : string Information about the fit to retrieve. This can be any of the following: - ``'fcn'``: `FCN` value at minimum, - ``'edm'``: estimated distance to minimum - ``'err_def'``: `Minuit` error matrix status code - ``'status_code'``: `Minuit` general status code ''' # declare vars in which to retrieve other info fcn_at_min = Double(0) edm = Double(0) err_def = Double(0) n_var_param = Long(0) n_tot_param = Long(0) status_code = Long(0) # Tell TMinuit to update the variables declared above self.__gMinuit.mnstat(fcn_at_min, edm, err_def, n_var_param, n_tot_param, status_code) if info == 'fcn': return fcn_at_min elif info == 'edm': return edm elif info == 'err_def': return err_def elif info == 'status_code': try: return D_MATRIX_ERROR[status_code] except: return status_code def get_chi2_probability(self, n_deg_of_freedom): ''' Returns the probability that an observed :math:`\chi^2` exceeds the calculated value of :math:`\chi^2` for this fit by chance, even for a correct model. In other words, returns the probability that a worse fit of the model to the data exists. If this is a small value (typically <5%), this means the fit is pretty bad. For values below this threshold, the model very probably does not fit the data. n_def_of_freedom : int The number of degrees of freedom. This is typically :math:`n_\text{datapoints} - n_\text{parameters}`. ''' chi2 = Double(self.get_fit_info('fcn')) ndf = Long(n_deg_of_freedom) return TMath.Prob(chi2, ndf) def get_contour(self, parameter1, parameter2, n_points=21): ''' Returns a list of points (2-tuples) representing a sampling of the :math:`1\\sigma` contour of the TMinuit fit. The ``FCN`` has to be minimized before calling this. **parameter1** : int ID of the parameter to be displayed on the `x`-axis. **parameter2** : int ID of the parameter to be displayed on the `y`-axis. *n_points* : int (optional) number of points used to draw the contour. Default is 21. *returns* : 2-tuple of tuples a 2-tuple (x, y) containing ``n_points+1`` points sampled along the contour. The first point is repeated at the end of the list to generate a closed contour. ''' self.out_file.write('\n') # entry in log-file self.out_file.write('\n') self.out_file.write('#'*(5+28)) self.out_file.write('\n') self.out_file.write('# Contour for parameters %2d, %2d #\n'\ %(parameter1, parameter2) ) self.out_file.write('#'*(5+28)) self.out_file.write('\n\n') self.out_file.flush() # # first, make sure we are at minimum self.minimize(final_fit=True, log_print_level=0) # get the TGraph object from ROOT g = self.__gMinuit.Contour(n_points, parameter1, parameter2) # extract point data into buffers xbuf, ybuf = g.GetX(), g.GetY() N = g.GetN() # generate tuples from buffers x = np.frombuffer(xbuf, dtype=float, count=N) y = np.frombuffer(ybuf, dtype=float, count=N) # return (x, y) def get_profile(self, parid, n_points=21): ''' Returns a list of points (2-tuples) the profile the :math:`\\chi^2` of the TMinuit fit. **parid** : int ID of the parameter to be displayed on the `x`-axis. *n_points* : int (optional) number of points used for profile. Default is 21. *returns* : two arrays, par. values and corresp. :math:`\\chi^2` containing ``n_points`` sampled profile points. ''' self.out_file.write('\n') # entry in log-file self.out_file.write('\n') self.out_file.write('#'*(2+26)) self.out_file.write('\n') self.out_file.write("# Profile for parameter %2d #\n" % (parid)) self.out_file.write('#'*(2+26)) self.out_file.write('\n\n') self.out_file.flush() # redirect stdout stream _redirection_target = None ## -- disable redirection completely, for now ##if log_print_level >= 0: ## _redirection_target = self.out_file with redirect_stdout_to(_redirection_target): pv = [] chi2 = [] error_code = Long(0) self.__gMinuit.mnexcm("SET PRINT", arr('d', [0.0]), 1, error_code) # no printout # first, make sure we are at minimum, i.e. re-minimize self.minimize(final_fit=True, log_print_level=0) minuit_id = Double(parid + 1) # Minuit parameter numbers start with 1 # retrieve information about parameter with id=parid pmin = Double(0) perr = Double(0) self.__gMinuit.GetParameter(parid, pmin, perr) # retrieve fitresult # fix parameter parid ... self.__gMinuit.mnexcm("FIX", arr('d', [minuit_id]), 1, error_code) # ... and scan parameter values, minimizing at each point for v in np.linspace(pmin - 3.*perr, pmin + 3.*perr, n_points): pv.append(v) self.__gMinuit.mnexcm("SET PAR", arr('d', [minuit_id, Double(v)]), 2, error_code) self.__gMinuit.mnexcm("MIGRAD", arr('d', [self.max_iterations, self.tolerance]), 2, error_code) chi2.append(self.get_fit_info('fcn')) # release parameter to back to initial value and release self.__gMinuit.mnexcm("SET PAR", arr('d', [minuit_id, Double(pmin)]), 2, error_code) self.__gMinuit.mnexcm("RELEASE", arr('d', [minuit_id]), 1, error_code) return pv, chi2 # Other methods ################ def fix_parameter(self, parameter_number): ''' Fix parameter number <`parameter_number`>. **parameter_number** : int Number of the parameter to fix. ''' error_code = Long(0) logger.info("Fixing parameter %d in Minuit" % (parameter_number,)) # execute FIX command self.__gMinuit.mnexcm("FIX", arr('d', [parameter_number+1]), 1, error_code) def release_parameter(self, parameter_number): ''' Release parameter number <`parameter_number`>. **parameter_number** : int Number of the parameter to release. ''' error_code = Long(0) logger.info("Releasing parameter %d in Minuit" % (parameter_number,)) # execute RELEASE command self.__gMinuit.mnexcm("RELEASE", arr('d', [parameter_number+1]), 1, error_code) def reset(self): '''Execute TMinuit's `mnrset` method.''' self.__gMinuit.mnrset(0) # reset TMinuit def FCN_wrapper(self, number_of_parameters, derivatives, f, parameters, internal_flag): ''' This is actually a function called in *ROOT* and acting as a C wrapper for our `FCN`, which is implemented in Python. This function is called by `Minuit` several times during a fit. It doesn't return anything but modifies one of its arguments (*f*). This is *ugly*, but it's how *ROOT*'s ``TMinuit`` works. Its argument structure is fixed and determined by `Minuit`: **number_of_parameters** : int The number of parameters of the current fit **derivatives** : C array If the user chooses to calculate the first derivative of the function inside the `FCN`, this value should be written here. This interface to `Minuit` ignores this derivative, however, so calculating this inside the `FCN` has no effect (yet). **f** : C array The desired function value is in f[0] after execution. **parameters** : C array A C array of parameters. Is cast to a Python list **internal_flag** : int A flag allowing for different behaviour of the function. Can be any integer from 1 (initial run) to 4(normal run). See `Minuit`'s specification. ''' # Retrieve the parameters from the C side of ROOT and # store them in a Python list -- resource-intensive # for many calls, but can't be improved (yet?) parameter_list = np.frombuffer(parameters, dtype=float, count=self.number_of_parameters) # call the Python implementation of FCN. f[0] = self.function_to_minimize(*parameter_list) def minimize(self, final_fit=True, log_print_level=2): '''Do the minimization. This calls `Minuit`'s algorithms ``MIGRAD`` for minimization and, if `final_fit` is `True`, also ``HESSE`` for computing/checking the parameter error matrix.''' # Set the FCN again. This HAS to be done EVERY # time the minimize method is called because of # the implementation of SetFCN, which is not # object-oriented but sets a global pointer!!! logger.debug("Updating current FCN") self.__gMinuit.SetFCN(self.FCN_wrapper) # Run minimization algorithm (MIGRAD + HESSE) error_code = Long(0) prefix = "Minuit run on" # set the timestamp prefix # insert timestamp self.out_file.write('\n') self.out_file.write('#'*(len(prefix)+4+20)) self.out_file.write('\n') self.out_file.write("# %s " % (prefix,) + strftime("%Y-%m-%d %H:%M:%S #\n", gmtime())) self.out_file.write('#'*(len(prefix)+4+20)) self.out_file.write('\n\n') self.out_file.flush() # redirect stdout stream _redirection_target = None if log_print_level >= 0: _redirection_target = self.out_file with redirect_stdout_to(_redirection_target): self.__gMinuit.SetPrintLevel(log_print_level) # set Minuit print level logger.debug("Running MIGRAD") self.__gMinuit.mnexcm("MIGRAD", arr('d', [self.max_iterations, self.tolerance]), 2, error_code) if(final_fit): logger.debug("Running HESSE") self.__gMinuit.mnexcm("HESSE", arr('d', [self.max_iterations]), 1, error_code) # return to normal print level self.__gMinuit.SetPrintLevel(self.print_level) def minos_errors(self, log_print_level=1): ''' Get (asymmetric) parameter uncertainties from MINOS algorithm. This calls `Minuit`'s algorithms ``MINOS``, which determines parameter uncertainties using profiling of the chi2 function. returns : tuple A tuple of [err+, err-, parabolic error, global correlation] ''' # Set the FCN again. This HAS to be done EVERY # time the minimize method is called because of # the implementation of SetFCN, which is not # object-oriented but sets a global pointer!!! logger.debug("Updating current FCN") self.__gMinuit.SetFCN(self.FCN_wrapper) # redirect stdout stream _redirection_target = None if log_print_level >= 0: _redirection_target = self.out_file with redirect_stdout_to(_redirection_target): self.__gMinuit.SetPrintLevel(log_print_level) logger.debug("Running MINOS") error_code = Long(0) self.__gMinuit.mnexcm("MINOS", arr('d', [self.max_iterations]), 1, error_code) # return to normal print level self.__gMinuit.SetPrintLevel(self.print_level) output = [] errpos=Double(0) # positive parameter error errneg=Double(0) # negative parameter error err=Double(0) # parabolic error gcor=Double(0) # global correlation coefficient for i in range(0, self.number_of_parameters): self.__gMinuit.mnerrs(i, errpos, errneg, err, gcor) output.append([float(errpos),float(errneg),float(err),float(gcor)]) return output
class MinimizerROOTTMinuit(MinimizerBase): def __init__(self, parameter_names, parameter_values, parameter_errors, function_to_minimize, tolerance=1e-9, errordef=MinimizerBase.ERRORDEF_CHI2, strategy=1): self._strategy = strategy self._par_bounds = np.array([None] * len(parameter_names)) self._par_fixed = np.array([False] * len(parameter_names)) self.reset() # sets self.__gMinuit and caches to None super(MinimizerROOTTMinuit, self).__init__(parameter_names=parameter_names, parameter_values=parameter_values, parameter_errors=parameter_errors, function_to_minimize=function_to_minimize, tolerance=tolerance, errordef=errordef) # -- private methods def _save_state(self): if self._par_val is None: self._save_state_dict["par_val"] = self._par_val else: self._save_state_dict["par_val"] = np.array(self._par_val) if self._par_err is None: self._save_state_dict["par_err"] = self._par_err else: self._save_state_dict["par_err"] = np.array(self._par_err) self._save_state_dict['par_fixed'] = np.array(self._par_fixed) self._save_state_dict['gMinuit'] = self.__gMinuit super(MinimizerROOTTMinuit, self)._save_state() def _load_state(self): self.reset() self._par_val = self._save_state_dict["par_val"] if self._par_val is not None: self._par_val = np.array(self._par_val) self._par_err = self._save_state_dict["par_err"] if self._par_err is not None: self._par_err = np.array(self._par_err) self._par_fixed = np.array(self._save_state_dict['par_fixed']) self.__gMinuit = self._save_state_dict['gMinuit'] # call the function to propagate the changes to the nexus: self._func_handle(*self.parameter_values) super(MinimizerROOTTMinuit, self)._load_state() def _recreate_gMinuit(self): self.__gMinuit = TMinuit(self.num_pars) self.__gMinuit.SetPrintLevel(-1) self.__gMinuit.mncomd("SET STRATEGY {}".format(self._strategy), ctypes.c_int(0)) self.__gMinuit.SetFCN(self._minuit_fcn) self.__gMinuit.SetErrorDef(self._err_def) # set gMinuit parameters error_code = ctypes.c_int(0) for _pid, (_pn, _pv, _pe) in enumerate( zip(self._par_names, self._par_val, self._par_err)): self.__gMinuit.mnparm(_pid, _pn, _pv, 0.1 * _pe, 0, 0, error_code) err_code = ctypes.c_int(0) # set fixed parameters for _par_id, _pf in enumerate(self._par_fixed): if _pf: self.__gMinuit.mnfixp(_par_id, err_code) # set parameter limits for _par_id, _pb in enumerate(self._par_bounds): if _pb is not None: _lo_lim, _up_lim = _pb self.__gMinuit.mnexcm( "SET LIM", arr('d', [_par_id + 1, _lo_lim, _up_lim]), 3, error_code) def _get_gMinuit(self): if self.__gMinuit is None: self._recreate_gMinuit() return self.__gMinuit def _migrad(self, max_calls=6000): # need to set the FCN explicitly before every call self._get_gMinuit().SetFCN(self._minuit_fcn) error_code = ctypes.c_int(0) self._get_gMinuit().mnexcm("MIGRAD", arr('d', [max_calls, self.tolerance]), 2, error_code) def _minuit_fcn(self, number_of_parameters, derivatives, f, parameters, internal_flag): """ This is actually a function called in *ROOT* and acting as a C wrapper for our `FCN`, which is implemented in Python. This function is called by `Minuit` several times during a fitters. It doesn't return anything but modifies one of its arguments (*f*). This is *ugly*, but it's how *ROOT*'s ``TMinuit`` works. Its argument structure is fixed and determined by `Minuit`: **number_of_parameters** : int The number of parameters of the current fitters **derivatives** : C array If the user chooses to calculate the first derivative of the function inside the `FCN`, this value should be written here. This interface to `Minuit` ignores this derivative, however, so calculating this inside the `FCN` has no effect (yet). **f** : C array The desired function value is in f[0] after execution. **parameters** : C array A C array of parameters. Is cast to a Python list **internal_flag** : int A flag allowing for different behaviour of the function. Can be any integer from 1 (initial run) to 4(normal run). See `Minuit`'s specification. """ # Retrieve the parameters from the C side of ROOT and # store them in a Python list -- resource-intensive # for many calls, but can't be improved (yet?) parameter_list = np.frombuffer(parameters, dtype=float, count=self.num_pars) # call the Python implementation of FCN. f[0] = self._func_wrapper(*parameter_list) def _calculate_asymmetric_parameter_errors(self): self._get_gMinuit().mnmnos() _asymm_par_errs = np.zeros(shape=(self.num_pars, 2)) for _n in range(self.num_pars): _number = Long(_n) _eplus = ctypes.c_double(0) _eminus = ctypes.c_double(0) _eparab = ctypes.c_double(0) _gcc = ctypes.c_double(0) self._get_gMinuit().mnerrs(_number, _eplus, _eminus, _eparab, _gcc) _asymm_par_errs[_n, 0] = _eminus.value _asymm_par_errs[_n, 1] = _eplus.value self.minimize() return _asymm_par_errs def _get_fit_info(self, info): '''Retrieves other info from `Minuit`. **info** : string Information about the fit to retrieve. This can be any of the following: - ``'fcn'``: `FCN` value at minimum, - ``'edm'``: estimated distance to minimum - ``'err_def'``: `Minuit` error matrix status code - ``'status_code'``: `Minuit` general status code ''' # declare vars in which to retrieve other info fcn_at_min = ctypes.c_double(0) edm = ctypes.c_double(0) err_def = ctypes.c_double(0) n_var_param = ctypes.c_int(0) n_tot_param = ctypes.c_int(0) status_code = ctypes.c_int(0) # Tell TMinuit to update the variables declared above self.__gMinuit.mnstat(fcn_at_min, edm, err_def, n_var_param, n_tot_param, status_code) if info == 'fcn': return fcn_at_min.value elif info == 'edm': return edm.value elif info == 'err_def': return err_def.value elif info == 'status_code': return status_code.value else: raise ValueError("Unknown fit info: %s" % info) # -- public properties @property def hessian(self): if not self.did_fit: return None if self._hessian is None: _submat = self._remove_zeroes_for_fixed(self.cov_mat) _submat_inv = 2.0 * self.errordef * np.linalg.inv(_submat) self._hessian = self._fill_in_zeroes_for_fixed(_submat_inv) return self._hessian.copy() @property def cov_mat(self): if not self.did_fit: return None if self._par_cov_mat is None: _n_pars_total = self.num_pars _tmp_mat_array = arr('d', [0.0] * (_n_pars_total**2)) # get parameter covariance matrix from TMinuit self._get_gMinuit().mnemat(_tmp_mat_array, _n_pars_total) # reshape into 2D array _sub_cov_mat = np.asarray(np.reshape( _tmp_mat_array, (_n_pars_total, _n_pars_total)), dtype=np.float) _num_pars_free = np.sum(np.invert(self._par_fixed)) _sub_cov_mat = _sub_cov_mat[:_num_pars_free, :_num_pars_free] self._par_cov_mat = self._fill_in_zeroes_for_fixed(_sub_cov_mat) return self._par_cov_mat.copy() @property def hessian_inv(self): if not self.did_fit: return None if self._hessian_inv is None: self._hessian_inv = self.cov_mat / (2.0 * self.errordef) return self._hessian_inv.copy() @property def parameter_values(self): return self._par_val.copy() @parameter_values.setter def parameter_values(self, new_values): self._par_val = np.array(new_values) self.reset() @property def parameter_errors(self): return self._par_err.copy() @parameter_errors.setter def parameter_errors(self, new_errors): _err_array = np.array(new_errors) if not np.all(_err_array > 0): raise ValueError("All parameter errors must be > 0! Received: %s" % new_errors) self._par_err = _err_array self.reset() # -- private "properties" # -- public methods def reset(self): super(MinimizerROOTTMinuit, self).reset() self.__gMinuit = None def set(self, parameter_name, parameter_value): if parameter_name not in self._par_names: raise ValueError("No parameter named '%s'!" % (parameter_name, )) _par_id = self.parameter_names.index(parameter_name) self._par_val[_par_id] = parameter_value self.reset() def fix(self, parameter_name): # set local flag _par_id = self.parameter_names.index(parameter_name) if self._par_fixed[_par_id]: return # par is already fixed self._par_fixed[_par_id] = True if self.__gMinuit is not None: # also update Minuit instance err_code = ctypes.c_int(0) self.__gMinuit.mnfixp(_par_id, err_code) # self.__gMinuit.mnexcm("FIX", # arr('d', [_par_id+1]), 1, error_code) self._invalidate_cache() def is_fixed(self, parameter_name): _par_id = self.parameter_names.index(parameter_name) return self._par_fixed[_par_id] def release(self, parameter_name): # set local flag _par_id = self.parameter_names.index(parameter_name) if not self._par_fixed[_par_id]: return # par is already released self._par_fixed[_par_id] = False if self.__gMinuit is not None: # also update Minuit instance self.__gMinuit.mnfree(-_par_id - 1) # self.__gMinuit.mnexcm("RELEASE", # arr('d', [_par_id+1]), 1, error_code) self._invalidate_cache() def limit(self, parameter_name, parameter_bounds): assert len(parameter_bounds) == 2 if parameter_bounds[0] is None or parameter_bounds[1] is None: raise MinimizerROOTTMinuitException( "Cannot define one-sided parameter limits when using the ROOT TMinuit Minimizer." ) # set local flag _par_id = self.parameter_names.index(parameter_name) if self._par_bounds[_par_id] == parameter_bounds: return # same limits already set if self._par_val[_par_id] < parameter_bounds[0]: self.set(parameter_name, parameter_bounds[0]) elif self._par_val[_par_id] > parameter_bounds[1]: self.set(parameter_name, parameter_bounds[1]) self._par_bounds[_par_id] = parameter_bounds if self.__gMinuit is not None: _lo_lim, _up_lim = self._par_bounds[_par_id] # also update Minuit instance error_code = ctypes.c_int(0) self.__gMinuit.mnexcm("SET LIM", arr('d', [_par_id + 1, _lo_lim, _up_lim]), 3, error_code) self._did_fit = False self._invalidate_cache() def unlimit(self, parameter_name): # set local flag _par_id = self.parameter_names.index(parameter_name) if self._par_bounds[_par_id] is None: return # parameter is already unlimited self._par_bounds[_par_id] = None if self.__gMinuit is not None: # also update Minuit instance error_code = ctypes.c_int(0) self.__gMinuit.mnexcm("SET LIM", arr('d', [_par_id + 1]), 1, error_code) self._did_fit = False self._invalidate_cache() def minimize(self, max_calls=6000): if np.all(self._par_fixed): raise MinimizerROOTTMinuitException( "Cannot perform a fit if all parameters are fixed!") self._migrad(max_calls=max_calls) # retrieve fitters parameters self._par_val = np.zeros(self.num_pars) self._par_err = np.zeros(self.num_pars) _pv, _pe = ctypes.c_double(0), ctypes.c_double(0) for _par_id in six.moves.range(0, self.num_pars): self.__gMinuit.GetParameter(_par_id, _pv, _pe) # retrieve fit result self._par_val[_par_id] = _pv.value self._par_err[_par_id] = _pe.value self._did_fit = True def contour(self, parameter_name_1, parameter_name_2, sigma=1.0, **minimizer_contour_kwargs): if not self.did_fit: raise MinimizerROOTTMinuitException( "Need to perform a fit before calling contour()!") _numpoints = minimizer_contour_kwargs.pop("numpoints", 100) if minimizer_contour_kwargs: raise MinimizerROOTTMinuitException( "Unknown parameters: {}".format(minimizer_contour_kwargs)) _id_1 = self.parameter_names.index(parameter_name_1) _id_2 = self.parameter_names.index(parameter_name_2) self.__gMinuit.SetErrorDef(sigma**2) _t_graph = self.__gMinuit.Contour(_numpoints, _id_1, _id_2) self.__gMinuit.SetErrorDef(self._err_def) _x_buffer, _y_buffer = _t_graph.GetX(), _t_graph.GetY() _N = _t_graph.GetN() _x = np.frombuffer(_x_buffer, dtype=float, count=_N) _y = np.frombuffer(_y_buffer, dtype=float, count=_N) self._func_handle(*self.parameter_values) return ContourFactory.create_xy_contour((_x, _y), sigma) def profile(self, parameter_name, bins=21, bound=2, args=None, subtract_min=False): if not self.did_fit: raise MinimizerROOTTMinuitException( "Need to perform a fit before calling profile()!") MAX_ITERATIONS = 6000 _error_code = ctypes.c_int(0) _minuit_id = Long(self.parameter_names.index(parameter_name) + 1) _par_min = ctypes.c_double(0) _par_err = ctypes.c_double(0) self.__gMinuit.GetParameter(_minuit_id - 1, _par_min, _par_err) _par_min = _par_min.value _par_err = _par_err.value _x = np.linspace(start=_par_min - bound * _par_err, stop=_par_min + bound * _par_err, num=bins, endpoint=True) self.__gMinuit.mnexcm("FIX", arr('d', [_minuit_id]), 1, _error_code) _y = np.zeros(bins) for i in range(bins): self.__gMinuit.mnexcm("SET PAR", arr('d', [_minuit_id, Double(_x[i])]), 2, _error_code) self.__gMinuit.mnexcm("MIGRAD", arr('d', [MAX_ITERATIONS, self.tolerance]), 2, _error_code) _y[i] = self._get_fit_info("fcn") self.__gMinuit.mnexcm("RELEASE", arr('d', [_minuit_id]), 1, _error_code) self._migrad() self.__gMinuit.mnexcm("SET PAR", arr('d', [_minuit_id, Double(_par_min)]), 2, _error_code) if subtract_min: _y -= self.function_value return np.asarray((_x, _y))
class MinimizerROOTTMinuit(MinimizerBase): def __init__(self, parameter_names, parameter_values, parameter_errors, function_to_minimize, strategy = 1): self._par_names = parameter_names self._strategy = strategy self._func_handle = function_to_minimize self._err_def = 1.0 self._tol = 0.001 # initialize the minimizer parameter specification self._minimizer_param_dict = {} assert len(parameter_names) == len(parameter_values) == len(parameter_errors) self._par_val = [] self._par_err = [] self._par_fixed_mask = [] self._par_limits = [] for _pn, _pv, _pe in zip(parameter_names, parameter_values, parameter_errors): self._par_val.append(_pv) self._par_err.append(_pe) self._par_fixed_mask.append(False) self._par_limits.append(None) # TODO: limits/fixed parameters self.__gMinuit = None # cache for calculations self._hessian = None self._hessian_inv = None self._fval = None self._par_cov_mat = None self._par_cor_mat = None self._par_asymm_err = None self._fmin_struct = None self._pars_contour = None self._min_result_stale = True self._printed_inf_cost_warning = False # -- private methods # def _invalidate_cache(self): # self._par_val = None # self._par_err = None # self._hessian = None # self._hessian_inv = None # self._fval = None # self._par_cov_mat = None # self._par_cor_mat = None # self._par_asymm_err_dn = None # self._par_asymm_err_up = None # self._fmin_struct = None # self._pars_contour = None def _recreate_gMinuit(self): self.__gMinuit = TMinuit(self.n_pars) self.__gMinuit.SetPrintLevel(-1) self.__gMinuit.mncomd("SET STRATEGY {}".format(self._strategy), Long(0)) self.__gMinuit.SetFCN(self._minuit_fcn) self.__gMinuit.SetErrorDef(self._err_def) # set gMinuit parameters error_code = Long(0) for _pid, (_pn, _pv, _pe) in enumerate(zip(self._par_names, self._par_val, self._par_err)): self.__gMinuit.mnparm(_pid, _pn, _pv, 0.1 * _pe, 0, 0, error_code) err_code = Long(0) # set fixed parameters for _par_id, _pf in enumerate(self._par_fixed_mask): if _pf: self.__gMinuit.mnfixp(_par_id, err_code) # set parameter limits for _par_id, _pl in enumerate(self._par_limits): if _pl is not None: _lo_lim, _up_lim = _pl self.__gMinuit.mnexcm("SET LIM", arr('d', [_par_id + 1, _lo_lim, _up_lim]), 3, error_code) def _get_gMinuit(self): if self.__gMinuit is None: self._recreate_gMinuit() return self.__gMinuit def _migrad(self, max_calls=6000): # need to set the FCN explicitly before every call self._get_gMinuit().SetFCN(self._minuit_fcn) error_code = Long(0) self._get_gMinuit().mnexcm("MIGRAD", arr('d', [max_calls, self.tolerance]), 2, error_code) def _hesse(self, max_calls=6000): # need to set the FCN explicitly before every call self._get_gMinuit().SetFCN(self._minuit_fcn) error_code = Long(0) self._get_gMinuit().mnexcm("HESSE", arr('d', [max_calls]), 1, error_code) def _minuit_fcn(self, number_of_parameters, derivatives, f, parameters, internal_flag): """ This is actually a function called in *ROOT* and acting as a C wrapper for our `FCN`, which is implemented in Python. This function is called by `Minuit` several times during a fitters. It doesn't return anything but modifies one of its arguments (*f*). This is *ugly*, but it's how *ROOT*'s ``TMinuit`` works. Its argument structure is fixed and determined by `Minuit`: **number_of_parameters** : int The number of parameters of the current fitters **derivatives** : C array If the user chooses to calculate the first derivative of the function inside the `FCN`, this value should be written here. This interface to `Minuit` ignores this derivative, however, so calculating this inside the `FCN` has no effect (yet). **f** : C array The desired function value is in f[0] after execution. **parameters** : C array A C array of parameters. Is cast to a Python list **internal_flag** : int A flag allowing for different behaviour of the function. Can be any integer from 1 (initial run) to 4(normal run). See `Minuit`'s specification. """ # Retrieve the parameters from the C side of ROOT and # store them in a Python list -- resource-intensive # for many calls, but can't be improved (yet?) parameter_list = np.frombuffer(parameters, dtype=float, count=self.n_pars) # call the Python implementation of FCN. f[0] = self._func_wrapper(*parameter_list) def _insert_zeros_for_fixed(self, submatrix): """ Takes the partial error matrix (submatrix) and adds rows and columns with 0.0 where the fixed parameters should go. """ _mat = submatrix # reduce the matrix before inserting zeros _n_pars_free = self.n_pars_free _mat = _mat[0:_n_pars_free,0:_n_pars_free] _fparam_ids = [_par_id for _par_id, _p in enumerate(self._par_fixed_mask) if _p] for _id in _fparam_ids: _mat = np.insert(np.insert(_mat, _id, 0., axis=0), _id, 0., axis=1) return _mat # -- public properties def get_fit_info(self, info): '''Retrieves other info from `Minuit`. **info** : string Information about the fit to retrieve. This can be any of the following: - ``'fcn'``: `FCN` value at minimum, - ``'edm'``: estimated distance to minimum - ``'err_def'``: `Minuit` error matrix status code - ``'status_code'``: `Minuit` general status code ''' # declare vars in which to retrieve other info fcn_at_min = Double(0) edm = Double(0) err_def = Double(0) n_var_param = Long(0) n_tot_param = Long(0) status_code = Long(0) # Tell TMinuit to update the variables declared above self.__gMinuit.mnstat(fcn_at_min, edm, err_def, n_var_param, n_tot_param, status_code) if info == 'fcn': return fcn_at_min elif info == 'edm': return edm elif info == 'err_def': return err_def elif info == 'status_code': try: return D_MATRIX_ERROR[status_code] except: return status_code @property def n_pars(self): return len(self.parameter_names) @property def n_pars_free(self): return len([_p for _p in self._par_fixed_mask if not _p]) @property def errordef(self): return self._err_def @errordef.setter def errordef(self, err_def): assert err_def > 0 self._err_def = err_def if self.__gMinuit is not None: self.__gMinuit.set_errordef(err_def) self._min_result_stale = True @property def tolerance(self): return self._tol @tolerance.setter def tolerance(self, tolerance): assert tolerance > 0 self._tol = tolerance self._min_result_stale = True @property def hessian(self): # TODO: cache this return 2.0 * self.errordef * np.linalg.inv(self.cov_mat) @property def cov_mat(self): if self._min_result_stale: raise MinimizerROOTTMinuitException("Cannot get cov_mat: Minimizer result is outdated.") if self._par_cov_mat is None: _n_pars_total = self.n_pars _n_pars_free = self.n_pars_free _tmp_mat_array = arr('d', [0.0]*(_n_pars_total**2)) # get parameter covariance matrix from TMinuit self.__gMinuit.mnemat(_tmp_mat_array, _n_pars_total) # reshape into 2D array _sub_cov_mat = np.asarray( np.reshape( _tmp_mat_array, (_n_pars_total, _n_pars_total) ) ) self._par_cov_mat = self._insert_zeros_for_fixed(_sub_cov_mat) return self._par_cov_mat @property def cor_mat(self): if self._min_result_stale: raise MinimizerROOTTMinuitException("Cannot get cor_mat: Minimizer result is outdated.") if self._par_cor_mat is None: _cov_mat = self.cov_mat # TODO: use CovMat object! # Note: for zeros on cov_mat diagonals (which occur for fixed parameters) -> overwrite with 1.0 _sqrt_diag = np.array([_err if _err>0 else 1.0 for _err in np.sqrt(np.diag(_cov_mat))]) self._par_cor_mat = np.asarray(_cov_mat) / np.outer(_sqrt_diag, _sqrt_diag) return self._par_cor_mat @property def hessian_inv(self): return self.cov_mat / 2.0 / self.errordef @property def parameter_values(self): return self._par_val @property def parameter_errors(self): return self._par_err @property def parameter_names(self): return self._par_names # -- private "properties" # -- public methods def fix(self, parameter_name): # set local flag _par_id = self.parameter_names.index(parameter_name) if self._par_fixed_mask[_par_id]: return # par is already fixed self._par_fixed_mask[_par_id] = True if self.__gMinuit is not None: # also update Minuit instance err_code = Long(0) self.__gMinuit.mnfixp(_par_id, err_code) # self.__gMinuit.mnexcm("FIX", # arr('d', [_par_id+1]), 1, error_code) self._min_result_stale = True def fix_several(self, parameter_names): for _pn in parameter_names: self.fix(_pn) def release(self, parameter_name): # set local flag _par_id = self.parameter_names.index(parameter_name) if not self._par_fixed_mask[_par_id]: return # par is already released self._par_fixed_mask[_par_id] = False if self.__gMinuit is not None: # also update Minuit instance self.__gMinuit.mnfree(-_par_id-1) # self.__gMinuit.mnexcm("RELEASE", # arr('d', [_par_id+1]), 1, error_code) self._min_result_stale = True def release_several(self, parameter_names): for _pn in parameter_names: self.release(_pn) def limit(self, parameter_name, parameter_bounds): assert len(parameter_bounds) == 2 # set local flag _par_id = self.parameter_names.index(parameter_name) if self._par_limits[_par_id] == parameter_bounds: return # same limits already set self._par_limits[_par_id] = parameter_bounds if self.__gMinuit is not None: _lo_lim, _up_lim = self._par_limits[_par_id] # also update Minuit instance error_code = Long(0) self.__gMinuit.mnexcm("SET LIM", arr('d', [_par_id+1, _lo_lim, _up_lim]), 3, error_code) self._min_result_stale = True def unlimit(self, parameter_name): # set local flag _par_id = self.parameter_names.index(parameter_name) if self._par_limits[_par_id] is None: return # parameter is already unlimited self._par_limits[_par_id] = None if self.__gMinuit is not None: # also update Minuit instance error_code = Long(0) self.__gMinuit.mnexcm("SET LIM", arr('d', [_par_id+1]), 1, error_code) self._min_result_stale = True def minimize(self, max_calls=6000): self._migrad(max_calls=max_calls) # retrieve fitters parameters self._par_val = [] self._par_err = [] _pv, _pe = Double(0), Double(0) for _par_id in six.moves.range(0, self.n_pars): self.__gMinuit.GetParameter(_par_id, _pv, _pe) # retrieve fitresult self._par_val.append(float(_pv)) self._par_err.append(float(_pe)) self._min_result_stale = False def contour(self, parameter_name_1, parameter_name_2, sigma=1.0, **minimizer_contour_kwargs): if self.__gMinuit is None: raise MinimizerROOTTMinuitException("Need to perform a fit before calling contour()!") _numpoints = minimizer_contour_kwargs.pop("numpoints", 100) if minimizer_contour_kwargs: raise MinimizerROOTTMinuitException("Unknown parameters: {}".format(minimizer_contour_kwargs)) _id_1 = self.parameter_names.index(parameter_name_1) _id_2 = self.parameter_names.index(parameter_name_2) self.__gMinuit.SetErrorDef(sigma ** 2) _t_graph = self.__gMinuit.Contour(_numpoints, _id_1, _id_2) self.__gMinuit.SetErrorDef(self._err_def) _x_buffer, _y_buffer = _t_graph.GetX(), _t_graph.GetY() _N = _t_graph.GetN() _x = np.frombuffer(_x_buffer, dtype=float, count=_N) _y = np.frombuffer(_y_buffer, dtype=float, count=_N) self._func_handle(*self.parameter_values) return ContourFactory.create_xy_contour((_x, _y), sigma) def profile(self, parameter_name, bins=21, bound=2, args=None, subtract_min=False): if self.__gMinuit is None: raise MinimizerROOTTMinuitException("Need to perform a fit before calling profile()!") MAX_ITERATIONS = 6000 _error_code = Long(0) _minuit_id = Long(self.parameter_names.index(parameter_name) + 1) _par_min = Double(0) _par_err = Double(0) self.__gMinuit.GetParameter(_minuit_id - 1, _par_min, _par_err) _x = np.linspace(start=_par_min - bound * _par_err, stop=_par_min + bound * _par_err, num=bins, endpoint=True) self.__gMinuit.mnexcm("FIX", arr('d', [_minuit_id]), 1, _error_code) _y = np.zeros(bins) for i in range(bins): self.__gMinuit.mnexcm("SET PAR", arr('d', [_minuit_id, Double(_x[i])]), 2, _error_code) self.__gMinuit.mnexcm("MIGRAD", arr('d', [MAX_ITERATIONS, self.tolerance]), 2, _error_code) _y[i] = self.get_fit_info("fcn") self.__gMinuit.mnexcm("RELEASE", arr('d', [_minuit_id]), 1, _error_code) self._migrad() self.__gMinuit.mnexcm("SET PAR", arr('d', [_minuit_id, Double(_par_min)]), 2, _error_code) return np.asarray((_x, _y))